Talk:Mass

"the attractive force all objects in the universe have for each other". The definition does not try to explain how these two seemingly unrelated phenomena can be related by this singular characteristic - "mass". It also does not even begin to explain what mass is -- how is arrises from an object. Omitting the fact that these basic questions about this basic phenomina is "sketchy" is to overstate our thin understanding. Addressing what we don't know is just as, if not more important than addressing what we do. Doing so stimulates the creative mind.

Under GR, the fact that inertial and gravitational mass are the same can be reduced to the "principle of the universality of free fall" - basically a symmetry argument. As for declaring our lack of knowledge: well, we have a mathematical description of inertial and gravity which works in all but the most extreme situations (black holes and the big bang). Don't you think that counts for something? Our understanding of mass is on roughly the same footing as our understanding of the other three forces. With any scientific theory, someone can find a fundamental principle or assumption and say "but you don't know why that is the case". Theories which don't have such assumptions or principles are non-scientific. -- Tim

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When I wrote standards and special provisions for the Connecticut Department of Transportation's Bridge Design Unit, we tried to make them complete, brief and easy to understand: I think the following statement defining mass is what we might might have written if we had been asked to do so:

Mass can be defined in terms of either (a) "the mutual resistance of two particles, bodies or masses of material matter from simultaneously occupying and/ or passing throught the exact same place" and/or (b) "the mutual resistance of the penetration of a body resting on a planet's terra firma surface." Where the bodies physically exert mutual force on each other and are accelerated - their velocities forcibly changed - inversely to their weight, and/or massiveness.

One body cannot exert more (mutual) force on the other's nor can one exert greater impulse's than the other's. The impenetrability of matter, is the principle that relates these two seemingly unrelated phenomea, and makes this a scientific theory.

Respectfully submitted, Donald G. Shead 54 Chaplin St, Chaplin CT 06235 e-mail <dcshead@charter.net>

Contents

1 Question about the origin of mass 2 Mass and Energy 3 Demostration on the Moon 4 Unit of mass eV or eV/c2 4.1 various books and their conventions for mass units 5 mass vs weight 6 Irrelevant references 7 Misleading?

Question about the origin of mass

The following is from the article on Standard_model: "Mass is really a coupling between a left handed fermion and a right handed fermion. For example, the mass of an electron is really a coupling between a left handed electron and a right handed electron, which is the antiparticle of a left handed positron. Also neutrinos show large mixings in their mass coupling, so it's not accurate to talk about neutrino masses in the flavor basis or to suggest a left handed electron neutrino and a right handed electron neutrino have the same mass as this table seems to suggest."

Does that make sense? If so, is there a way to expand on it in some way that would make sense to non-experts? JWSchmidt 21:52, 25 Mar 2004 (UTC)

Mass and Energy

This discussion started in WikiProject Science.

I quote:

Mass is now considered as one form of energy, i.e. mass can sometimes disappears into energy, and some energy can be converted to mass.

This is what I mean by a "totally wrong section on mass-energy equivalence". The article already points out the following:

Historically, the term "mass" was used for the quantity E/c². This was called the "relativistic mass", and m called the "rest mass". This terminology is now discouraged by physicists, because there is no need for two terms for the energy of a particle, and because it creates confusion when speaking of "massless" particles.

The issue is not one of whether amateurs are allowed to contribute to science articles; of course they are, but I should hope that they take the trouble to make sure the contributions are actually correct! -- CYD

I happen to believe that this statement is "perfectly good" and publishable, although it may not be perfectly phrased (remember, it's coming from an amateur, and amateurs are allowed to edit). The statement is substantiated by the Einstein article, for example, which says: matter and energy are simply different forms of the same substance, and A simple calculation using the mass of the uranium nuclei and the masses of the products of nuclear fission reveals that large amounts of energy are released upon fission. Could you then propose another phrasing that is both correct and understandable by regular readers like me ? (or do you expect regular readers of the encyclopedia to understand the 'relativistic mass' jargon ? Sorry, I don't) Pcarbonn 18:46, 1 Oct 2004 (UTC)

I've corrected the Einstein article. By the way, here is a 1948 quote from Einstein. -- CYD

It is not good to introduce the concept of the mass M = m /(1-v²/c²)^1/2 of a body for which no clear definition can be given. It is better to introduce no other mass than `the rest mass' m. Instead of introducing M, it is better to mention the expression for the momentum and energy of a body in motion. -- Albert Einstein

You may be right, but then, the equivalence between mass and energy is such a prevalent notion that it should be clearly discussed so that anybody can understand it. Let's work on it together (but not today, I have no time). Pcarbonn 06:07, 2 Oct 2004 (UTC)

It looks like you did not need me ! Congratulations for a job well done ! Pcarbonn 19:17, 4 Oct 2004 (UTC)

Demostration on the Moon

The demostration of equivalance of the time of falling object was carried out before the "Apollo 15 Moon walk". It was carried out a lots of times (it even was a classical laboratory experiment) in a vacum tube. I have not a precise date for the first experiment (I suppose it was in XVII or XVIII century since the vacum technique was enougth good at the time for this experiment). The demostration on the Moon is obviously a very spectacural one, but it is not hte first. Even more also the experiments in the vacum were very spectacular centuries ago, when people was not used to vacum technique. AnyFile 19:23, 26 Oct 2004 (UTC)

Unit of mass eV or eV/c²

In unit measure it should pointed out that the use in particle Physics to use electron volts came out from the equivalence between mass and energy (in the meanig this equivlence means). In rigid way the unit to be used should be eV/c2</sub> (eV is an utnit of Energy, not Mass), but for shortness it is wrtitten eV only (giving for sure that who reads knows how the equivalence works) AnyFile 19:25, 26 Oct 2004 (UTC)

I agree. I have added a sentence with some explanation of this. -Lethe | Talk

In actual practice, I think most people use "eV". Saying that "eV/c^2" is more "correct" is nonsense; a unit is simply a ratio between one quantity and another fixed quantity, and as long as the fixed quantity is unambiguously defined you can do whatever you want (e.g. physicists measure time in units of distance all over the place, setting c=1). As the article already noted, using eV as a unit of mass relies on there being a precise equivalence between (rest) mass and (rest) energy. —Steven G. Johnson 23:01, Dec 3, 2004 (UTC)

Using eV/c² as a unit of mass relies on the equivalence of mass and rest energy. Using eV as a unit of mass relies on both the equivalence of mass and energy AND the choice of units in which c=1. I know you agree with this, because you said the same exact thing in your comment. This distinction should be made clear in the article. I don't understand your reasoning, and am inclined to bring back my edits. -Lethe | Talk

Not really. Using eV as a unit of mass merely relies on there being a well-defined mass associated with 1 eV, to which all other quantities are referenced. Of course, you then have to use consistent units for force, etc., but that's no real obstacle. (If you also use eV for energy, that implies c=1, but it's conceptually a separate question. You could "just as easily" use eV for mass and Joules for energy.) —Steven G. Johnson 02:37, Dec 4, 2004 (UTC)

(Philosophical arguments aside, the real question is what people use in practice. In practice, I think the answer is "eV". —Steven G. Johnson)

OK, so I agree that if we decided to use units where we want to use eV for mass, then eV are good units for mass, regardless of what assumptions we make about the units for energy (and therefore value of c). However, I think this is specious reasoning. No one thinks that eV is a unit for mass. In fact, eV is defined to be the amount of energy that an electron blah blah blah... The article text even mentions it thus: "it is common in particle physics to measure mass in terms of electron volts (eV), a unit of energy". eV is a unit of energy, and we are allowed to use it as a unit of mass only when we use both mass-energy equivalence and the units where c=1. I remain unconvinced by your argument. I still feel that a reader who strolls into this page who isn't very familiar with these units and the usage of mass-energy equivalence might be confused by the usage here without explanation, someone who perhaps came from a textbook that uses eV/c². I do know of textbooks which use those units throughout, so you must admit that even if you don't use them, there are physicists who prefer eV/c² for mass and eV for energy, at least for didactic purposes (and I do think that one of the main purposes of an encyclopedia should be didactic. So your approach to units is against at least some physicists. I wonder if we can get a third opinion in here? -Lethe | Talk

(see comment below...resetting indenting —Steven G. Johnson)

I'd be interested to know what textbook uses eV/c².

Sources provided below -Lethe | Talk 04:49, Dec 7, 2004 (UTC)

The fact is that many experimental particle physics papers use eV as a unit of mass (I just did a quick lit. search to confirm this). e.g. Phys. Rev. Lett. 83 (1), 41 (1999): "We thus exclude an effective Majorana neutrino mass greater than 0.2 eV...". Or Phys. Rev. Lett. 85 (17), 3568 (2000): "Super-Kamiokande can detect an electron neutrino mass as small as 1.8 eV, and the proposed OMNIS detector can detect mu and tau neutrino masses as small as 6 eV."

Not just experimental particle physics. Everyone who isn't teaching undergrads uses eV as a unit for mass. The question which I am disputing here is whether all these physicists in the world are using eV as a unit of mass because they're scale is fucked up, or because in units where c=1, mass and energy have the same units. My point all along is that it is the latter. -Lethe | Talk 04:49, Dec 7, 2004 (UTC)

As for the purpose of Wikipedia, the purpose of the aside about eV was to describe the kinds of units that are used in practice, and we aren't serving readers by saying eV/c² when people actually use eV (which also happens to be a unit of energy). —Steven G. Johnson 02:32, Dec 6, 2004 (UTC)

Okay, I found an older PRL that uses eV/c² (Phys. Rev. Lett. 46 (2), 80 (1981)). I concede that people also use eV/c² in practice.

I am not arguing that people use eV/c² in practice (maybe they once did, but these days, no one does, in my experience), what I am arguing is that everyone in the world uses units of mass for mass, and units of energy for energy, and never the twain shall meet, unless they happen to also be using units where c=1 (natural units). See the sources below. -Lethe | Talk 04:49, Dec 7, 2004 (UTC)

The question is, what will serve readers more — to learn that there is more than one unit of mass (obvious), or that it is perfectly possible and even convenient to use a unit of energy also as a unit of mass? —Steven G. Johnson 02:41, Dec 6, 2004 (UTC)

For whatever it's worth, I'm with Stevenj on this one. It's not as though the article doesn't explain how to convert this energy unit into kilograms. -- CYD

It's worth something. I did, afterall, ask for a third opinion, and so I'm glad you gave one (and sad that it didn't agree with mine). Since I'm now in the minority here, if you and Steven aren't convinced after my last attempt, I'm going to give up and go home and cry. -Lethe | Talk 04:49, Dec 7, 2004 (UTC)

(This reminds me of a funny story, by the way. An experimental colleague of mind told me about an exciting result that one of the theorists at his university predicted...he proceeded to do the eperiment, and after taking great pains he was unable to observe the result. He went back to the theorist and asked him what was wrong...the theorist went back over his work and came back the next day to apologize: "I know what happened, sorry - I accidentally left out a factor of c²." So, the predicted effect was actually 16 orders of magnitude smaller. —Steven G. Johnson)

various books and their conventions for mass units

these first couple of undergraduate textbooks use MeV/c² as their mass units. So we see that for didactic purposes (teaching undergrads), explicit mass units are prefered.

• Williams (1991). Nuclear and Particle Physics. Clarendon Press, Oxford
• Povh, Rith, Scholz, Zetsche (1999). Particles and Nuclei. Springer Verlag.
• Griffiths (1987). Introduction to Elementary Particles. John Wiley & Sons.

This last book has the most enlightening explanation of this choice of units, which I quote here:

"typical energies in particle physics are MeV, GeV or even TeV. Momenta are measured in MeV/c (or GeV/c, or whatever), and masses in MeV/c². Thus the proton weighs 938 MeV/c²=1.67x10^-24"

"Actually, particle theorists are lazy (or clever, depending on your point of view - they seldom include the c's and the ℏ's in their formulas. You're just supposed to fit them in for yourself at the end, to make the dimensions come out right. As they say in the business, “set c=ℏ=1”. This amounts to working in units such that time is measured in centimeters and mass and energy in inverse centimeters."

Another undergrad textbook (Martin & Shaw (1997). Particle Physics. John Wiley & Sons.) which does use MeV for mass says:

"In practice [...] Energies are measured in MeV, GeV etc., while momenta are MeV/c etc. and masses are MeV/c² etc. This should be compared with natural units, where energy, momentum and mass all have the same dimension of energy, and are all measured in, for example, MeV."

So teachers who use MeV/c² for mass and teachers who use MeV for mass both agree: we are allowed to use MeV only by virtue of units where c=1.

You're confusing two issues. If you use MeV for both energy and mass, then that does imply c=1 units (unless you alter the equations of motion). And, indeed, that choice of both units is common. However, it is two independent choices of units. —Steven G. Johnson

Hmm... So you know, when you say it that way, I think I'm coming around to your point of view; I think you are right. So if you choose to measure mass and energy both in energy units (saying that they are both energy units means that [E]/[m] is a dimensionless number), this forces c to be a dimensionless number (the square root of [E]/[m]), but unless [E] and [m] are the same unit, then c will not be 1. Right? So we could choose [m]=eV and [E]=MeV, and then c would equal 1000. -Lethe | Talk 08:18, Dec 11, 2004 (UTC)

Now for some more advanced books:

• Weinberg (1995). The Quantum Theory of Fields, Vol I. Cambridge University Press.
• Polchinski (1998). String Theory, Vol I. Cambridge University Press.

The first one says about units only "Except in Chapter 1, we use units with ℏ and the speed of light taken to be unity." and the second says even more succinctly "The constants ℏ and c are set to 1."

So particle theorists agree: we are allowed to use MeV only by virtue os units where c=1.

Don't put words in their mouths. They say that they use c=1 units (and I agree that these are almost universal with theorists), but your books don't claim that these are required for eV units of mass. I agree that the two choices are strongly correlated in practice, and indeed it is convenient to pair them, but that's a different issue. (See above regarding what the undergrad. texts say.) —Steven G. Johnson

OK, you're right, they never claimed that this choice of units was required. But you should at least concede that this convention (using eV/c^2 for mass in units where c is not 1, and using eV for mass in units where c=1, the former sometimes preferred for teaching, the latter for doing physics) is a sort of textbook standard, and so deviating from it, while not bad, deserves mention. Actually, I guess you did already concede that point, more or less. -Lethe | Talk 08:18, Dec 11, 2004 (UTC)

The upshot of all this as I see it is this: in practice, all sensible people use eV for mass, but not because they feel like using an arbitrary scale for mass, but rather for the reason that these people are all working in units where c=1. No source I have ever seen thinks that they can use eV for mass without setting c=1. The whole concept of natural units and using eV/c² is already confusing for undergrads, it is my position that the idea of using eV for mass without explicitly stating that this may be done only by virtue of using units where c=1 will be even more confusing for those kinds of readers. -Lethe | Talk 04:49, Dec 7, 2004 (UTC)

I'm afraid that's false. In actual practice, as opposed to undergraduate textbooks that apparently oversimplify matters, people use whatever units are convenient for a given quantity, independent of what units they use for other quantities. As long as you combine them in appropriate ratios (which is what units really are: ratios), you are fine. For example, in the 2000 Phys. Rev. Lett. article I quoted above, in a single equation they use time in seconds, distance in parsecs, mass in MeV, and mass in ktons. It is an experimental paper, and c=1 "theorist units" appear nowhere. (Distance is always in cm or parsecs and time is always in seconds or ms.) —Steven G. Johnson 05:48, Dec 7, 2004 (UTC)

This argument is going nowhere. The article seems to have changed in the meantime; does anyone have any objections or suggestions to Stevenj's new "units of mass" section? -- CYD

I enjoy a good disagreement.-Lethe | Talk 08:18, Dec 11, 2004 (UTC)

mass vs weight

I'm not sure what they do in commerce, but I'm pretty sure that the typical measure of body weight in humans via a bathroom scale, for example, is weight, not mass. If you take the same scale to the moon, and put the same person in it, the scale will read a smaller number. They are essentially springs measuring the force. They measure weight, not mass.

Also, why do you say "an object will exert more force" in a stronger gravitational field? This is true, but rather irrelevant. Weight is the force that your planet exerts on you. and that's what the scale measures.

Finally, what's with the clause "the quantity the weight we use in commerce"? I can't quite convince myself that this clause is grammatical. Can you parse it for me? Lethe | Talk 18:24, Feb 4, 2005 (UTC)

Have you ever turned back a paycheck because you do so little work, Lethe? How about you, CYD? I'd bet that the jargon usage there doesn't cause either of you any difficulty. Why, then, do you have such great problems understanding similar ambiguities in the word weight?

If you are pretty sure about the issue of human weight, then you obviously haven't put much thought into it at all.

• What happens when you get serious about your weight, and go weigh yourself on one of those beam balances at the doctor's office or the gym? Isn't that a better indication of what you want to measure, than some substitute we put up with in our homes because it is cheap?

• What happens in your little thought experiment about taking these scales to the moon? Those balances are mass-measuring devices, not force measuring devices. Those cheap bathroom scales (which didn't even exist until 1937) are no more accurate in measuring force than thay are in measuring mass on Earth. If you hop on your mother's bathroom scale, and it reads 5 lb or even 5 kg less than your bathroom scale at home, you don't automatically credit it to success of your weight-loss diet, do you?

• Of course, those pounds and kilograms, units of mass, are what people use when they weigh themselves, all around the world. Or stones, and while there are kilograms-force and pounds-force, I've never heard of any stone-force.

Even in the United States, many hospitals measure body weight in kilograms. Often, they can even measure this weight in either pounds or kilograms. But hospitals like to be more accurate, not having variations between the scales in different departments, or if a patient is transferred to a different hospital.

• So how do you think those hospitals calibrate their scales? They place a test weight (an object of known mass, exerting an unknown and irrelevant amount of force due to gravity) on the scale and compare its known mass to the scale's reading. Nobody ever calibrates these scales differently for measuring pounds than they do for measuring kilograms, either. In fact, it is often the same scale that can measure both—either by flipping the bar on those old balance beams, to get a different set of detents for the weights, or by a constant conversion factor (the same anywhere in the world) programmed into modern electronic-readout scales.
• NASA doctors use the same terminology their counterparts with Earth-bound patients use, when they study "weight loss" of astronauts in space, etc.

Then, of course, there is our Body Mass Index; weight in kilograms, divided by the square of height in meters. Or, as the article puts it "(This is 703.07 times the weight in pounds, divided by the square of the height in inches.)" Once again, note the constant conversion factor. If the kilograms and pounds were measures of different things, we'd need a variable there.

Here are some of standards organizations on this point. American Society for Testing and Materials, Standard for Metric Practice, E 380-79, ASTM 1979:

• 3.4.1.2 Considerable confusion exists in the use of the term weight as a quantity to mean either force or mass. In commercial and everyday use, the term weight nearly always means mass; thus, when one speaks of a person's weight, the quantity referred to is mass.

NIST Guide for the Use of the International System of Units (SI), section 8.3 (http://physics.nist.gov/Pubs/SP811/sec08.html#8.3)

• Thus the SI unit of the quantity weight used in this sense is the kilogram (kg) and the verb "to weigh" means "to determine the mass of" or "to have a mass of."

Examples: the child's weight is 23 kg

I'll fix the typos in the language you didn't understand this time around.
Gene Nygaard 22:53, 4 Feb 2005 (UTC)

My edition of Webster's Encyclopedic Dictionary says:

weight (weit) 1. n. the force acting on a body in a gravitational field, equal to the product of its mass and the acceleration of the body produced by the field. Strictly speaking, the value for the acceleration due to gravity depends upon position in the gravitational field and thus weight depends on where it is measured. However, since the value of the acceleration due to gravity is approximately equal (9.8m/sec²) everywhere on the surface of the earth, and exactly the same when measured at different times but in the same place, this factor is often neglected. The value of the mass (with mass units) is often used instead, to mean the force (weight) on an object of given mass measured at the surface of the earth.

-- CYD

Irrelevant references

I deleted the mass of references to "relativistic mass" because it's simply irrelevant to the article. The article should introduce relativistic mass, explain what it is, how it is used, and why many physicists don't like it, and move on. Listing a bunch of introductory textbooks and popular physics books that refer to relativistic mass does absolutely nothing for the reader. What needs to be said, is already said:

Some authors define a quantity known as the relativistic mass, which is basically the quantity E/c2. This makes the "equivalence" of "mass" and energy true by definition, though neither quantity is frame-independent! "Relativistic mass" was used in many early writings on relativity, and it is still used in books for laymen as well as introductory physics classes.

How is this "pretending that relativistic mass doesn't exist", as User:Gene Nygaard claimed? -- CYD

The general tone of this article was getting to be at the stage of a sham notion that relativistic mass is never used, and deleting the specific examples someone added is one step in getting back to that. Much of the quoted part above has had to be added back in after overzealous editing by the ones who would like to pretend that relativistic mass doesn't exist, or even that it is somehow "incorrect", and especially that it is never used any more. In particular, if this "moving on" part, it is very misleading to simply say that:

• "E = mc² is not a "good" relativistic statement; it is true only in the rest frame of the object."

This is especially bad because of the use of the term "relativistic" as an adjective modifying statement. That sentence is only true if mass is used to mean invariant mass, not if mass means relativistic mass. That's one reason why these comments had to be added at this point in the article. Gene Nygaard 15:49, 3 May 2005 (UTC)

A significant part of the point is that, even if all, or almost all, working physicists use invariant mass today, no significant change has been made unless and until they make the effort of selling this idea to the rest of the world. The use of E = m c⊃ in both popular literature and in introductory textbooks, a use in the general sense and not in the sense which is only true "in the rest frame", is one example of the still very common use of relativistic mass. The references CYD has been blanking, of course, include not only popular literature, but professional journals as well, showing that even the notion that no physicists use relativistic mass any more is a falsehood. Gene Nygaard 16:03, 3 May 2005 (UTC)

Please indicate the statement in the article that says that relativistic mass is never used. I could throw in an equally large list of references to articles that specifically don't use relativistic mass; but, as I already mentioned, that would be belaboring the point.

Have you bothered actually reading the article? All the points you bring up are already in there -- it is clearly stated that the equation E = mc² is correct in all frames provided you make m the relativistic mass, though it also points out that neither side is a frame invariant quantity. -- CYD

It is still mentioned in *Relativistic mass* that "it was realized that the invariant mass was the more useful quantity and people stopped referring to the relativistic mass altogether" This statement is either a result of intellectual blunder or intellectual dishonesty. -- AlphonsusW

Then edit that article; don't mess up this one. -- CYD

Misleading?

I do not understand this (end of the first section):

if one were to treat inertial mass mi, passive gravitational mass mp, and active gravitational mass ma distinctly, Newton's law of universal gravitation would take the form <math>m_ia=\frac{Gm_pm_a}{r^2}<math>.

Are there implicitely two bodies? What is r? It seems misleading to me and if you agree, I would like to remove it. --Philipum 13:41, 27 May 2005 (UTC)

Yes, there are two bodies. Newton's Law of Universal Gravitation states that the gravitational force between two bodies is inversely proportional to the square of the distance between them. That explains the r². You haven't said what is misleading about this statement, only that it is unclear. Why do you want it removed? -Lethe | Talk 17:39, May 27, 2005 (UTC)

I suppose I find it misleading because it gives the impression to be a bizarre way to define the different mass concepts of inertial mass, passive gravitational mass, and active gravitational mass. I also react against the asymmetry of the expression: it gives the impression that we have a mass that creates the field and a mass that feels it, but in reality both masses play both roles. Removing it would not make any harm since the laws of gravitation are explained in more details later in the article. --Philipum 06:35, 30 May 2005 (UTC)